Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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![**Educational Worksheet: Radian and Degree Measure**
**Section 1: Degree to Radian Conversion**
Convert each degree measure to radian measure in terms of π. Provide exact answers and do not round. Show all your work.
1. \( 36^\circ \)
\[
\frac{36 \pi}{180} = \frac{\pi}{5}
\]
2. \( -250^\circ \)
3. \( -145^\circ \)
4. \( 870^\circ \)
5. \( 18^\circ \)
6. \( -820^\circ \)
**Section 2: Radian to Degree Conversion**
Convert each radian measure to degree measure. Round to one decimal place if needed. Show all your work.
7. \( \frac{13\pi}{30} \)
8. \( 4\pi \)
9. \( -\frac{2\pi}{5} \)
10. \( \frac{3\pi}{16} \)
11. \( -\frac{7\pi}{9} \)
12. \( -1 \)
**Section 3: Determining the Quadrant**
Determine the quadrant in which the terminal side of the angle lies. Make a quick sketch to justify your answer. If the angle is given in degrees, work in degrees; if the angle is given in radians, work in radians.
13. \( -156^\circ \)
14. \( 371^\circ \)
15. \( -\frac{5\pi}{3} \)
**Explanation of Given Example**:
- For problem 1:
\( 36^\circ \) is converted to radians by using the formula:
\[
\text{Radians} = \frac{\text{Degrees} \times \pi}{180}
\]
So,
\[
\frac{36 \times \pi}{180} = \frac{\pi}{5}
\]
Feel free to solve the provided exercises. If sketches or graphs are necessary, ensure they are accurate and neat to help visualize the problem solutions effectively.](https://content.bartleby.com/qna-images/question/00c239b2-49f2-4118-83c1-4fc31b3c935a/f04b7f86-ab21-43b9-ac0b-f7203819c5e4/gut9xe_processed.jpeg)
Transcribed Image Text:**Educational Worksheet: Radian and Degree Measure**
**Section 1: Degree to Radian Conversion**
Convert each degree measure to radian measure in terms of π. Provide exact answers and do not round. Show all your work.
1. \( 36^\circ \)
\[
\frac{36 \pi}{180} = \frac{\pi}{5}
\]
2. \( -250^\circ \)
3. \( -145^\circ \)
4. \( 870^\circ \)
5. \( 18^\circ \)
6. \( -820^\circ \)
**Section 2: Radian to Degree Conversion**
Convert each radian measure to degree measure. Round to one decimal place if needed. Show all your work.
7. \( \frac{13\pi}{30} \)
8. \( 4\pi \)
9. \( -\frac{2\pi}{5} \)
10. \( \frac{3\pi}{16} \)
11. \( -\frac{7\pi}{9} \)
12. \( -1 \)
**Section 3: Determining the Quadrant**
Determine the quadrant in which the terminal side of the angle lies. Make a quick sketch to justify your answer. If the angle is given in degrees, work in degrees; if the angle is given in radians, work in radians.
13. \( -156^\circ \)
14. \( 371^\circ \)
15. \( -\frac{5\pi}{3} \)
**Explanation of Given Example**:
- For problem 1:
\( 36^\circ \) is converted to radians by using the formula:
\[
\text{Radians} = \frac{\text{Degrees} \times \pi}{180}
\]
So,
\[
\frac{36 \times \pi}{180} = \frac{\pi}{5}
\]
Feel free to solve the provided exercises. If sketches or graphs are necessary, ensure they are accurate and neat to help visualize the problem solutions effectively.
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